plumiInverse hyperbolic functions: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 8.2 Inverse hyperbolic functions, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 6 questions on Inverse hyperbolic functions, as a list
- June 2025, Pure Core 1, Q2 (5 marks): - b y d in terms of x. l, find x 1 1 2 (a) Given that y cosh x [1] = d 3 - b l at the point where x 1 1 (b) Determine an equation of the normal to the curve y c
- June 2024, Pure Core 1, Q7 (9 marks): - , show that (a) By using the definitions of cosh u and sinh u in terms of eu and e u 7 sinh 2 u 2 sinh cosh u u . [2] / The equation of a curve, C, is y 16 co
- June 2023, Pure Core 2, Q3 (6 marks): ^ h d 1 1 3 (a) Show that sinh - u . [2] = u d 2 u 1 + 1 (b) Find the equation of the normal to the graph of y sinh - 2 x at the point where x 6 . = = Give your
- June 2022, Pure Core 2, Q5 (7 marks): (a) By using the exponential definitions of sinh x and cosh x, prove the identity 2 2 cosh 2 x cosh x sinh x . [2] / + (b) Hence find an expression for cosh 2x
- November 2021, Pure Core 2, Q5 (8 marks): In this question you must show detailed reasoning. 2 (a) Using the definition of cosh x in terms of exponentials, show that cosh 2 x 2 cosh x - . [2] 1 / (b) So
- November 2020, Pure Core 2, Q9 (11 marks): Two thin poles, OA and BC, are fixed vertically on horizontal ground. A chain is fixed at A and C such that it touches the ground at point D as shown in the dia
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